| 1 | Jan 16 |
1.1. Complex numbers and the complex plane |
| 2 | Jan 18 |
1.2. Some geometry |
| 3 | Jan 23 |
1.3. Subsets of the plane |
| 4 | Jan 25 |
1.4. Functions and limits |
| 5 | Jan 30 |
1.5. The exponential, logarithm and trigonometric functions |
| 6 | Feb 1 |
1.6. Line integrals and Green's theorem |
| 7 | Feb 6 |
2.1. Analytic and harmonic functions; the Cauchy-Riemann equations |
| 8 | Feb 8 |
2.2. Power series |
| 9 | Feb 13 |
2.3. Cauchy's theorem and Cauchy's formula |
| 10 | Feb 15 |
Review and catch up |
| 11 | Feb 20 |
Midterm 1 |
| 12 | Feb 22 |
2.4. Consequences of Cauchy's formula |
| 13 | Feb 27 |
2.4. Continued |
| 14 | Mar 1 |
2.5. Isolated singularities |
| 15 | Mar 6 |
2.5. Laurent series |
| 16 | Mar 8 |
2.6. The residue theorem. |
| 17 | Mar 20 |
2.6. Applications of the residue theorem |
| 18 | Mar 22 |
3.1. The zeros of an analytic function |
| 19 | Mar 27 |
3.2. Maximum modulus and mean value |
| 20 | Mar 29 |
Review and catch up. |
| 21 | Apr 3 |
Midterm 2 |
| 22 | Apr 5 |
3.3. Linear fractional transformations |
| 23 | Apr 10 |
3.4. Conformal mapping |
| 24 | Apr 12 |
3.5. The Riemann Mapping Theorem and Schwarz-Christoffel Transformations |
| 25 | Apr 17 |
4.1. Harmonic functions |
| 26 | Apr 19 |
The Gamma function |
| 27 | Apr 24 |
The Riemann zeta function |
| 28 | Apr 26 |
Review and catch up. |
| May 4 |
Final Exam 8-11 AM |